4000

MATE-4001 Curso Tutorial de Maestria

The objective of this course is for students to develop a study and research plan proposed in advance under the guidance of a professor from the Department.

Credits

4

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MATE-4002 Curso Tutorial Postgrado 2

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4

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MATE-4038 Prog. Funcional y Aplicaciones

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4

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MATE-4070 Curso Nivelatorio Para El Posgrado de Ingeniería Bio-Médica

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4

Distribution

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MATE-4101 Algebra Conmutativa

Rings and Ideals. Modules. Rings and fraction modules. Primary decomposition. Whole dependence and valuations. Chain conditions. Noetherian rings. Artin rings. Discrete valuation rings and Dedeking rings. Completions. Theory of dimension and, if there is time left, other themes that the professor may deem convenient.

Credits

4

Distribution

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Instructor

Onshuus Niño Alf

MATE-4103 Teoría Algebraica de Números

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4

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MATE-4106 Álgebra para posgrado

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4

MATE-4116 Combinatoria de Determinantes

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4

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MATE-4120 Lógica Matemática

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4

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MATE-4127 Topología Dócil y Estructuras O-Minimales

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4

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MATE-4130 Teoría de Conjuntos 2

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4

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- MATE-4137

MATE-4140 Teoría de Modelos 1

Initiate studies of Model Theory of First-Order Logics. Completitude, Compacity, Lowenheim-Skolem Theorems, Categorical K-Theory, Complete Theories, Decidable and Undecidable Theory, Elementary Equivalence and Summersion. Characterization of Universal Theories, Universal-Existential. Existentially Closed Models, Complete Model Theories, Elimination of Quantifiers, Partial Isomorphisms, Feferman-Vaugth Theorems. Interpolation and Definibility Theorems. Automorphisms, Indiscernible, Ehrenfeucht-Mostowski Theorem. Fraissé Generic Models. Boolean Algebra, Filters, Ultra filters. Ultra products, Ultra product Saturation. Types of Elements, Types Realization and Omission, Saturation, Homogeneity, Universality. Atomic and Prime Models, Omega-Categoric Theories. Type Spaces, Stability, Stable Omega Theories. Keisler-Shelah Theorem, Characterization of Elementary Classes. Morley Categoricity Theorem. Baldwin-Lachlan Theorem. After all of the foregoing, the instructor may concentrate further on themes such as: Laws 0-1 in Finite Models. Finite Models Spectrum. Relations with Complexity.

Credits

4

Distribution

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Instructor

Corredor Londoño Luis

MATE-4141 Teoria de Modelos 2

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4

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MATE-4147 MATE-4147

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MATE-4157 Introducción A Las Representaciones de Grupos Finitos

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4

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MATE-4158 Geometría Algebraica Computacional

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4

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- MATE-4161

- MATE-4172

MATE-4173 Algebra Abstracta 2

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4

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MATE-4175 Introduccion a la Geometria Algebraica

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4

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MATE-4176 Grupo `Amenable"

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4

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MATE-4181 Complejidad Computacional

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4

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MATE-4201 Análisis para posgrado

Credits

4

MATE-4205 Teoría Ergódica

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4

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MATE-4210 Analisis Complejo

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4

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MATE-4220 Medida e Integración

Algebras and sigma-algebras, measures, Lebesgue Measure, Constitution and regularity. integrated functions: Roles measurable properties almost everywhere, the definition of integral, theorems of boundaries, Riemann integral, complex functions and extent of image. Convergence: Modes of convergence, regulated spaces, Lp spaces, dual spaces. Real and complex measures: Absolute continuity, singularity, functions of bounded variation, dual spaces Lp. Product measures: construction, Fubini Theorem, applications.

Credits

3

Distribution

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Instructor

Berenstein Opscholtens Alexander

MATE-4241 Operator Theory

Credits

4

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MATE-4242 Análisis Armónico Abstracto

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4

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MATE-4301

MATE-4303 Funciones Generalizadas

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4

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MATE-4330 Analisis Funcional

Banach Spaces: Definitions and examples. Subspaces, linear transformations, quotient spaces. Duality: Hahn-Banach’s theorem. Banach-Steinhaus’ theorems, the Open Mapping and the Closed Graph theorems. Applications: Adjoint operators. Hilbert Spaces: Definitions and examples, orthogonality. Continuous operators: Operator convergence. Hermetian, normal and unitary operations. Orthogonal projections. Compact operators: Introduction to spectral theory.

Credits

3

Distribution

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MATE-4331 Teoría Espectral de Operadores

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4

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MATE-4361 Análisis Asintótico

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4

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MATE-4401 MATE-4401

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MATE-4403 Clases Características

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4

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- MATE-4412

MATE-4421 Topología Algebraica

Introduce the basic concepts of algebraic topology, and the classical algebraic tools used in the calculation of topological invariants of spaces simplicials. Content: Variety topological. Homotopy group fundamental properties. Building simplicials, homology, Ulama-Borsuk theorem, fixed point theorem Lefschetz, Cohomology, Poincare duality. Theory of beams, Prebeams, Resolutions. Fiber vector.

Credits

4

Distribution

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Instructor

Malakhaltsev Mikhail

MATE-4424 Topologia Algebraica 2

Credits

4

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MATE-4426 Grupos de Lie

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4

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MATE-4430 Variedades Toricas I

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4

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MATE-4431 Variedades Toricas 2

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4

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MATE-4441 MATE-4441

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MATE-4523 Estadística No Paramétrica y Remuestreo

Credits

4

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MATE-4530 MATE-4530

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MATE-4533 MATE-4533

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- MATE-4706

MATE-4707 MATE-4707

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MATE-4710 Matemáticas Financieras

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4

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MATE-4716 Optimización Combinatoria

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4

Distribution

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MATE-4717 Introducción A la Teoría de Control

Credits

4

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MATE-4754 Teoría de Colas

Credits

4

Distribution

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MATE-4901 Seminario de Postgrado I

The objective of the course is to place students in contact with a wide range of advanced mathematical topics and teach them to synthesize and orally explain these topics with clarity and accuracy.

Credits

2

Distribution

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Instructor

Ould Ahmed

MATE-4902 Seminario de Postgrado II

The objective of the course is to place students in contact with a wide range of advanced mathematical topics and teach them to synthesize and orally explain these topics with clarity and accuracy. In this seminar, students decide on the topic in the area they would like to do their graduation thesis and prepare a presentation on this topic with the professor who will possibly be the director of the graduation thesis.

Credits

2

Distribution

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Instructor

Ould Ahmed

MATE-4903 Seminario de Trabajo de Grado

The objective of this course is to introduce students to research activities, through the direct study of specialized mathematical literature and train them, not only to solve problems but also to formulate them properly. Students will present their theses to the Graduate and Research Committee of the Department before the last week of withdrawals for the semester. Students are expected to move forward in their research during the following period.

Credits

3

Distribution

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MATE-4904 Trabajo de Grado

Students will carry out a research project in one of the mathematical areas offered by the Master’s Program. This is to demonstrate that the author has assimilated and systematized or carried out thorough exploration of a particular topic, showing evidence of a certain degree of creativity and great familiarity with recent information on the topic. The Graduation Thesis must be written in Spanish or English and have the formal organization expected of a scientific paper.

Credits

12

Distribution

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Instructor

Uribe Jongbloed Bernardo

MATE-4990 Inscripción a Grado

Credits

0

Distribution

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- MATE-4998